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受欢迎的三角函数 >

8cos(2x-5)=3

解答

8 cos (2 x - 5) = 3

解答

x = πn + \frac{5}{2} + \frac{1.18639 \dots}{2}, x = π + πn + \frac{5}{2} - \frac{1.18639 \dots}{2}

+1

度数

x = 177.22729 \dots^{\circ} + 18 0^{\circ} n, x = 289.25160 \dots^{\circ} + 18 0^{\circ} n

求解步骤

8 cos (2 x - 5) = 3

两边除以

8

8 cos (2 x - 5) = 3

两边除以

8

\frac{8 cos ( 2 x - 5 )}{8} = \frac{3}{8}

化简

cos (2 x - 5) = \frac{3}{8}

cos (2 x - 5) = \frac{3}{8}

使用反三角函数性质

cos (2 x - 5) = \frac{3}{8}

cos (2 x - 5) = \frac{3}{8}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 x - 5 = arccos (\frac{3}{8}) + 2 πn, 2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

2 x - 5 = arccos (\frac{3}{8}) + 2 πn, 2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

解

2 x - 5 = arccos (\frac{3}{8}) + 2 πn : x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

2 x - 5 = arccos (\frac{3}{8}) + 2 πn

将

5

到右边

2 x - 5 = arccos (\frac{3}{8}) + 2 πn

两边加上

5

2 x - 5 + 5 = arccos (\frac{3}{8}) + 2 πn + 5

化简

2 x = arccos (\frac{3}{8}) + 2 πn + 5

2 x = arccos (\frac{3}{8}) + 2 πn + 5

两边除以

2

2 x = arccos (\frac{3}{8}) + 2 πn + 5

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

化简

\frac{2 x}{2} = \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2} : πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

\frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

对同类项分组

= \frac{5}{2} + \frac{2 πn}{2} + \frac{arccos ( \frac{3}{8} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{5}{2} + πn + \frac{arccos ( \frac{3}{8} )}{2}

对同类项分组

= πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

解

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn : x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

将

5

到右边

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

两边加上

5

2 x - 5 + 5 = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

化简

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

两边除以

2

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

化简

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2} : π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

\frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

对同类项分组

= \frac{5}{2} + \frac{2 π}{2} + \frac{2 πn}{2} - \frac{arccos ( \frac{3}{8} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{5}{2} + π + πn - \frac{arccos ( \frac{3}{8} )}{2}

对同类项分组

= π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}, x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

以小数形式表示解

x = πn + \frac{5}{2} + \frac{1.18639 \dots}{2}, x = π + πn + \frac{5}{2} - \frac{1.18639 \dots}{2}

作图

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